Solve the Quadratic Equation: Find x in x² - 20 = 5

Q: Why are there two answers when I solve x² = 25?

Because both positive and negative numbers give the same result when squared! Since $ 5^2 = 25 $ and $ (-5)^2 = 25 $, both x = 5 and x = -5 are correct solutions.

Q: Do I always get two solutions for quadratic equations?

Not always! When the equation is $ x^2 = 0 $, you only get one solution: x = 0. And if you have something like $ x^2 = -4 $, there are no real solutions because you can't take the square root of a negative number.

Q: How do I know which sign to use in my final answer?

Use both signs! Write your answer as $ x = ±5 $ or list them separately: x = 5 and x = -5. Both values make the original equation true.

Q: What if the number under the square root isn't a perfect square?

Leave it as a square root! For example, if $ x^2 = 7 $, then $ x = ±\sqrt{7} $. You can use a calculator to find the decimal approximation if needed.

Q: Can I check my answer by substituting back?

Absolutely! Substitute both x = 5 and x = -5 into the original equation $ x^2 - 20 = 5 $. You should get $ 25 - 20 = 5 $ for both values.

Quadratic Equations with Square Root Solutions

Solve the following exercise:

$x^2-20=5$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Isolate X

00:13 Extract root

00:17 When extracting a root there are always 2 solutions (positive, negative)

00:20 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$x^2-20=5$

Step-by-step solution

To solve this quadratic equation $x^2 - 20 = 5$ , we will follow these steps:

Step 1: First, add 20 to both sides of the equation to isolate the $x^2$ term:

$x^2 - 20 + 20 = 5 + 20$

This simplifies to:

$x^2 = 25$

Step 2: Next, take the square root of both sides to solve for $x$ :

$x = \pm \sqrt{25}$

$x = \pm 5$

Therefore, the solutions to the equation are:

$x = 5$ and $x = -5$

Thus, the correct answer choice is:

$\pm 5$ from the provided options.

The correct solution to the problem is $\pm 5$ .

Final Answer

±5

Key Points to Remember

Essential concepts to master this topic

Isolation: Move constants to one side to isolate the x² term
Square Root: Take √ of both sides: $\sqrt{x^2} = \sqrt{25}$
Verification: Check both solutions: $(-5)^2 = 25$ and $(5)^2 = 25$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting the negative solution when taking square roots
Don't write x = 5 only when solving $x^2 = 25$ = missing half the answer! When you square both +5 and -5, you get 25, so both are valid solutions. Always write $x = ±\sqrt{25}$ to capture both solutions.

Practice Quiz

Test your knowledge with interactive questions

Solve the following equation:

$$ 2x^2-8=x^2+4 $$

FAQ

Everything you need to know about this question

Why are there two answers when I solve x² = 25?

Because both positive and negative numbers give the same result when squared! Since $5^2 = 25$ and $(-5)^2 = 25$ , both x = 5 and x = -5 are correct solutions.

Do I always get two solutions for quadratic equations?

Not always! When the equation is $x^2 = 0$ , you only get one solution: x = 0. And if you have something like $x^2 = -4$ , there are no real solutions because you can't take the square root of a negative number.

How do I know which sign to use in my final answer?

Use both signs! Write your answer as $x = ±5$ or list them separately: x = 5 and x = -5. Both values make the original equation true.

What if the number under the square root isn't a perfect square?

Leave it as a square root! For example, if $x^2 = 7$ , then $x = ±\sqrt{7}$ . You can use a calculator to find the decimal approximation if needed.

Can I check my answer by substituting back?

Absolutely! Substitute both x = 5 and x = -5 into the original equation $x^2 - 20 = 5$ . You should get $25 - 20 = 5$ for both values.

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